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Kazemi","submitted_at":"2014-07-12T08:36:25Z","abstract_excerpt":"For any integer $k\\geq 1$ and any graph $G=(V,E)$ with minimum degree at least $k-1$, we define a function $f:V\\rightarrow \\{0,1,2\\}$ as a Roman $k$-tuple dominating function on $G$ if for any vertex $v$ with $f(v)=0$ there exist at least $k$ and for any vertex $v$ with $f(v)\\neq 0$ at least $k-1$ vertices in its neighborhood with $f(w)=2$. The minimum weight of a Roman $k$-tuple dominating function $f$ on $G$ is called the Roman $k$-tuple domination number of the graph where the weight of $f$ is $f(V)=\\sum_{v\\in V}f(v)$.\n  In this paper, we initiate to study the Roman $k$-tuple domination num"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.3363","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-12T08:36:25Z","cross_cats_sorted":[],"title_canon_sha256":"f67e28becf86d488610b7dfa171c03072f465d35c29e31d4308fa3312a2d6e9f","abstract_canon_sha256":"6e3f1cdfb7386a78df5024c3c89ea7b8d645357319ce26b9d5866e30571a898d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:16.373086Z","signature_b64":"W5ZAe3DBNoqpQ4GIBiMkT4uSrLCc8o7EqYoxn3m5X3fMmGLA7OwqNJYE5Boy9Hs1Tvemq6flako+vooqbv57Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89a48b0c4d6667fb362f02c3ee166bca0fba4dcd9ee47274a2d7642bff2bf290","last_reissued_at":"2026-05-17T23:47:16.372531Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:16.372531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Roman k-tuple domination number of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adel P. 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